There is a strong case for making notes during problem solving.
Here are some of the more obvious reasons:
- Writing notes helps managing complexity: You can split a problem into parts, you can collect several approaches and deal with them one after the other etc.
- Notes document your thoughts – for later scrutiny, for resuming a chain of thought later – and sometimes for posterity.
- Notes can help to combine text and diagrams. The human brain is well equipped to deal with words and images, and either representation allows the application of quite different tools: In texts, you can ask questions, formulate alternatives, associate verbal concepts etc., in diagrams, you can add lines, rearrange items etc.
So making notes during problem solving is well worth a trial.
This leads to the question:
How to make notes most cleverly?
I’m sure this is an important topic in solving problems in general and in solving mathematical problems in particular – and one that is too often neglected.
The process of “tool mapping” described here is but one answer to this question (albeit hopefully a well thought-out one).